LT166 charging problem?

Hey y'all.
I went to cut my grass for the first time since buying it privately a week ago. It drove into the shed with no problems that day but this weekend it wouldn't start. I tried to jump the battery to the starter solenoid, no sparks or anything, so I jumped it with my car. When I turned it off to cool down it would'nt restart.

My question is, how do I tell if its the battery or the charging system?

Welcome to GTTAlk. The fact that it started when boosted means that you have a dead battery. The question is this. Is the battery bad or is the charging system not working. I would try to charge the battery and see if it will hold a charge. If you can prove the battery is good then the charging system is the culprit. I would check the wiring to make sure the connections from the charging system are good. Also make sure you have a good connection from the battery- terminal to the engine chassis. Look for any fuses that might be blown. Let us know what you find.